The limits of the rotating wave approximation in the electromagnetic field propagation in a cavity

Abstract

We consider three two-level atoms inside a one-dimensional cavity, interacting with the electromagnetic field in the rotating wave approximation (RWA), commonly used in the atom-radiation interaction. One of the three atoms is initially excited, and the other two are in their ground state. We numerically calculate the propagation of the field spontaneously emitted by the excited atom and scattered by the second atom, as well as the excitation probability of the second and third atom. The results obtained are analyzed from the point of view of relativistic causality in the atom-field interaction. We show that, when the RWA is used, relativistic causality is obtained only if the integrations over the field frequencies are extended to $-\infty$; on the contrary, noncausal tails remain even if the number of field modes is increased. This clearly shows the limit of the RWA in dealing with subtle problems such as relativistic causality in the atom-field interaction.

13 pages, 6 figures

References in corpus (2)

• Electromagnetically induced transparency and reduced speeds for single photons in a fully quantized model
• Manifestation of classical wave delays in a fully quantized model of the scattering of a single photon

Cited by in corpus (6)

• Causality issues of particle detector models in QFT and Quantum Optics
• The Rotating-Wave Approximation: Consistency and Applicability from an Open Quantum System Analysis
• Exploiting the Photonic Non-linearity of Free Space Subwavelength Arrays of Atoms
• Probabilities and signalling in quantum field theory
• Nonlocality of the energy density of a spontaneously emitted single-photon from a Hydrogen atom
• Fermi two-atom problem: non-perturbative approach via relativistic quantum information and algebraic quantum field theory